A biology quiz consists of 14 multiple-choice questions. Nine must be answered correctly to receive a passing grade. If each question has 4 possible answers,what is the probability that a student who guesses at random will pass?

3 Answers
Dec 2, 2017

0.0022

Explanation:

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Dec 2, 2017

#0.002154#

Explanation:

#C(14,9) (1/4)^9 (3/4)^5 + C(14,10) (1/4)^10 (3/4)^4 + C(14,11) (1/4)^11 (3/4)^3 + C(14,12) (1/4)^12 (3/4)^2 + C(14,13) (1/4)^13 (3/4) + (1/4)^14 = 0.001812 + 0.000302 + 0.000037 + 0.000003 + 0.000000 + 0.000000 = 0.002154#

#C(n,k) = (n!) / ((n-k)!k!)#

Dec 2, 2017

#0.0022#

Explanation:

This is Binomial with #n= 14, p= 1/4 = 0.25# and you need to find this probability:

#P(X >= 9)# = Sum from #x=9# to #x = 14: 14Cx (0.25^x)(0.75)^(14-x)#

If you some all 6 terms of this Binomial you will get the answer:

#P(X >= 9) = 0.0022#